The q-Dobinski formula may be interpreted as the average of powers of random variable X q with the q-Poisson distribution. Forty years ago Rota G. C. [1] proved the exponential generating function for Bell numbers B n to be of the form ∞ n=0 x n n! (B n) = exp(e x − 1) (1) using the linear functional L such that L(X n) = 1, n ≥ 0 (2) Then Bell numbers (see: formula (4) in [1]) are defined by L(...
